What is the excess pressure inside a bubble of soap solution of radius 500 mm, given that the surface tension of soap solution at the temperature `(20^(@)C)` is `2.50xx10^(-2)Nm^(-1)`? If an air bubble of the same dimension were formed at depth of 40.0 cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble? (1 atmospheric pressure is `1.01xx10^(5)Pa`).

Explanation

`r = 5 m m = 5 xx 10^(-3) m, sigma = 2.5 xx 10^(-2) Nm^(-1)`
Excess pressure `p = ( 4 sigma )/( r ) =( 4 xx 2.5 xx 10^(-2))/( 5 xx 10^(-3)) = 20 Pa`
Excess pressure inside an air bubble under soap solution
`p. = ( 2 sigma )/( R ) = ( 2 xx 2.5 xx 10^(-2) )/( 5 xx 10^(-3)) = 10 Pa`
Density of soap solution `= R.D. xx 1000 = 1.2 xx 1000 = 1200 kgm^(-3)`
Pressure inside the bubble = atmospheric pressure `+` pressure due to soap
solution of height 40 cm `+` Excess pressure
`= 1.01 xx 10^(5) + h rho g + p.`
`= 1.01 xx 10^(5) + 0.4 xx 1200 xx 9.8 + 10 = 105714 Pa`